Question

how to find the integration int (sinh^-1x)dx

Answer 1

it equals ln(x+sqrt(x^2+1))

Answer 2

thats the derivative...lol

Answer 3

i need the procedure.......whatever be the ans...

Answer 4

i have books where the ans is given but not the procedure......

Answer 5

ack!!...sinh^-1x = ln(x+sqrt(x^2+1))

Answer 6

integrate the ln function; is that possible?

Answer 7

There is a better way, substitute x = sinh(z). Then you can integrate by hand, because only terms of the form exp(z) and z exp(z) remain.

Answer 8

I get \[z\cosh z - \sinh z = \sqrt{1+x^2}\sinh^{-1} x - x\] can that be correct?

Answer 9

oh wait, you have to exchange sinh and cosh there ;-) but then it's correct. Yeah that substitution works :-)